What amount of 20% Salicylic Acid (in WSP) and WSP should be combined to produce 100 g of 5% Salicylic Acid?

Question

BlackTom AI · Accepted Answer

Conservation of active ingredient (salicylic acid) is the key: the total grams of salicylic acid contributed by components must equal the grams required in the final 100 g of 5% product.

1. Relevant knowledge points and concepts
- Percent concentration as mass fraction: % = (mass of active / total mass) × 100.
- Mass balance: mass of active in final blend = sum of mass of active from each component.
- WSP (the diluent) contains 0% salicylic acid; the salicylic ointment contains 20% salicylic acid.

2. Step-by-step reasoning
Let x = grams of 20% salicylic ointment needed. Then (100 − x) = grams of WSP.
Mass of salicylic acid from the ointment = 0.20 × x.
Mass of salicylic acid in final product must be 5% of 100 g = 5 g.
Set up the equation: 0.20 × x = 5.

3. Calculations (all intermediate steps)
0.20 x = 5
x = 5 / 0.20
x = 25 g
WSP mass = 100 − x = 100 − 25 = 75 g

4. Why the correct answer is correct
Using 25 g of the 20% ointment provides 0.20 × 25 = 5 g of salicylic acid. Dispersing that 5 g in a total of 100 g yields 5/100 = 0.05 = 5% final concentration. The WSP supplies no active, so 75 g WSP + 25 g 20% ointment produces exactly 100 g of 5% salicylic acid.

5. Why other options are incorrect (briefly)
- a: 80 g of 20% → 0.20×80 = 16 g active → 16% final, not 5%.
- b: 40 g of 20% → 0.20×40 = 8 g → 8% final.
- d: 60 g of 20% → 12 g → 12% final.
- e: 50 g of 20% → 10 g → 10% final.
None give the required 5 g active.

6. Conclusion
The correct mixture is 75 g WSP and 25 g of 20% salicylic ointment, matching answer c.

What amount of 20% Salicylic Acid (in WSP) and WSP should be combined to produce 100 g of 5% Salicylic Acid?Single choice

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